'I can't talk on the radio at all': Alison Mosshart, photographed in London last month for the Observer. Photograph: Antonio Zazueta Olmos

Some musicians wear their commitment to rock'n'roll like a series of battle scars. Queens of the Stone Age's Josh Hommehas the place and time of his worst ever gig tattooed on his forearm. Alison Mosshart, one half of the Kills and powerful frontwoman of Jack White's band the Dead Weather, celebrated her first appearance with long-term musical partner Jamie Hince by inking herself with "14-02-02". The famous tat, on her hand, is actually tiny – more like a serial number – but she's a formidable presence in spray-on trousers in a Dalston pub today. She's just designed a leather jacket for the Parisian fashion group Surface to Air, inspired by a photo of Lou Reed, which features an unusual stiff collar that acts like a windbreak if you happen to be out burning rubber.

It's hard to imagine Mosshart blazing up Dalston's Balls Pond Road, though. "How many speed bumps do we need, people?" she says. "The most boring place to be in a car – in the world – is this city. Sometimes I feel like I'm going to explode."

She's been in London since 2000, when she left her native Florida to join the Kills. She and Hince lived together in Dalston – "not any more, obviously," she says with cartoon sulkiness, "not now that he's married" [to Kate Moss]. Theirs remains one of the most enigmatic partnerships in rock: Mosshart was "best woman" at the wedding two years ago, and afterwards all three were seen holding hands. Like Jack White, she's an expert at boy/girl ambiguity, drawing it out for the sake of the band dynamic. "Jamie is my musical soulmate," she confirms. "Nothing ever felt so right."

Mosshart will take over Jarvis Cocker's Sunday Service on 6Music this month with three shows exploring the grand themes of love, outlaws and death and the devil in song. "I can't talk on the radio at all," she volunteers cheerily. "When the red light comes on, my hands go up in the air: I think they're trying to get to my face, to shut me up. I don't talk on stage for the same reason."

She deliberately didn't listen to Cocker's show in case it put her off. "This is like doing an art piece," she says. "I listened to love songs for 24 hours straight yesterday. And I got into categorisation problems – what's the difference between an "outlaw" and a "criminal"? Can I play a song about Charles Manson [Song For Charles Manson by Fiji]? He was basically an outlaw on Spahn Ranch. I'm getting obsessed, and I have other stuff to do."

That stuff includes travelling back and forth to Nashville, where she's bought a "muscle car" and finally has access to the open road she craves. She's writing new Kills songs at the wheel – "literally, with a pen and a paper. Believe me, it's so dangerous..."